In the present work, low energy incomplete fusion (ICF) in which only a part of projectile fuses with target nucleus has been investigated in terms of various entrance channel parameters. The ICF strength function has been extracted from the analysis of experimental excitation functions (EFs) measured for different projectile-target combinations from near- to well above- barrier energies in 12C,16O(from 1.02Vb to 1.64Vb)+169Tm systems. Experimental EFs have been analysed in the framework statistical model code PACE4 based on the idea of equilibrated compound nucleus decay. It has been found that the value of ICF fraction (FICF) increases with incident projectile energy. A substantial fraction of ICF (FICF ≈ 7 %) has been accounted even at energy as low as ≈ 7.5% above the barrier (at relative velocity νrel ≈0.027) in 12C+169Tm system, and FICF ≈ 10 % at νrel ≈0.014 in 16O+169Tm system. The probability of ICF is discussed in light of the Morgenstern’s mass-asymmetry systematics. The value of FICF for 16O+169Tm systems is found to be 18.3 % higher than that observed for 12C+169Tm systems. Present results together with the re-analysis of existing data for nearby systems conclusively demonstrate strong competition of ICF with CF even at slightly above barrier energies, and strong projectile dependence that seems to supplement the Morgenstern’s systematics.